The midpointM of VW has coordinates (9,4). Point W has coordinates (10,8). Find the coordinates of point V.Write the coordinates as decimals or integers.V=(_,_)
Q. The midpoint M of VW has coordinates (9,4). Point W has coordinates (10,8). Find the coordinates of point V.Write the coordinates as decimals or integers.V=(_,_)
Understand Midpoint Formula: Understand the midpoint formula and the given information.The midpoint formula for a line segment with endpoints (x1,y1) and (x2,y2) is (2x1+x2,2y1+y2). We are given the midpoint M(9,4) and one endpoint W(10,8). We need to find the coordinates of the other endpoint V(x1,y1).
Set Up Equations: Set up the equations for the midpoint based on the given information.The midpoint M is the average of the coordinates of V and W. Therefore, we have the following equations:(9,4)=(2x1+10,2y1+8)
Solve for x-coordinate: Solve for the x-coordinate of point V.Using the x-coordinate of the midpoint, we have:9=2x1+10Multiply both sides by 2 to clear the fraction:18=x1+10Subtract 10 from both sides to solve for x1:x1=18−10x1=8
Solve for y-coordinate: Solve for the y-coordinate of point V.Using the y-coordinate of the midpoint, we have:4=2y1+8Multiply both sides by 2 to clear the fraction:8=y1+8Subtract 8 from both sides to solve for y1:y1=8−8y1=0
Combine Coordinates: Combine the coordinates to form the point V. We have found that the x-coordinate of V is 8 and the y-coordinate of V is 0. Therefore, the coordinates of point V are (8,0).
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